Metamorphic Testing (MT) is a test design approach that produces “follow-up” test cases from existing ones, through the application of metamorphic relations (MRs). These MRs encode known properties about the problem being solved by the system under test. Identifying , designing and implementing the MRs is costly and error-prone. In the past, several methodologies have been proposed to guide the design of MRs, such as iterative metamorphic testing (IMT) or MR-GEN. In this paper, we propose a refinement of IMT which takes advantage of mature existing constraint programming languages to formalize MRs and automate the generation of test cases. The methodology covers the design of the initial cases, the design of the MRs, and the application of the MRs to produce a comprehensive test suite. METRECoP is applied to an empirical study, creating 10 MRs (by constraint solvers), producing a test suite that can detect all the defects that were seeded into the program, and guiding the design of additional MRs.